x - 2y > 4 and x > 4

Draw the graphs of the boundary lines whose equations are
found by replacing the inequality symbols with equal signs.

x - 2y = 4   
     x = 4

Graph the first line x - 2y = 4
It has intercepts (4,0) and (0,-2)



Now we pick a test point that is not on the line to determine
which side of the line is to be shaded.

The easiest test point is the origin (0,0). so we substitute it in

   x - 2y > 4
 0 - 2(0) > 4
        0 > 4

This is false, so we shade the side of the line that
the origin (0,0) is NOT on. That is, we shade the lower side
of the green line.

Now we draw the other boundary line:

x = 4

This is a vertical line parallel to the y-axis and 4 units right
of it:



Using the origin (0,0) as a test point again, we substitute it in

x > 4
0 > 4

This is fals so we are to shade the side of the vertical line which
the origin (0,0) is NOT on.  That is the right side of the line.

So we must shade the region which is below the green dotted line and
to the right of the black dotted line:

 


Edwin